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Byteland is an island with a number of cities connected by two-way roads. Road network is designed in such a way, that there is exactly one possibility to drive between any pair of cities (without turning back).
Unfortunately, hard times have come - Byteland is preparing for a war. The Lead Strategiest of Byteland is preparing a plan of defence of Byteland, which takes into account creation of a special security zone. The zone will be created by blocking some of the existing roads in Byteland in such a way, that it won't be possible to drive through these roads. In order to make the zone completely secure, following rules have to be fulfilled:
Write a program which:
The first line of the standard input contains one integer (), representing the number of cities in Byteland. Cities are numbered with numbers .
Each of the following lines of the standard input contains pair of integers () separated with single space. Pair represents a direct road connecting cities and . Each pair of cities is connected with at most one direct road.
In the following line of the standard input there is an integer () - it is the number of queries to process. Each of the following lines contains one integer (). It represents query number - the number of cities that have to be inside 'th special security zone.
Your program should write to the standard output exactly numbers, each of them in a separate line. The number in 'th line should be:
For the input data:
7 1 2 1 3 2 4 2 5 3 6 3 7 2 2 3
the correct result is:
Task author: Marek Turski.